GIFSQ Tools · Module 16 — Statistics, Experimental Design & Research · Tool 307 of 500
Analyse a balanced two-factor experiment: the main effect of each factor, their interaction, and the error — the workhorse of factorial food-process trials (Fisher ANOVA, ISO 16269-1).
Try sample values — fills the form with the worked example below.
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F — factor A
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F — factor B
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F — interaction A×B
Equation: SST = SSA + SSB + SSAB + SSE. SSA = b·r·Σ(x̄ᵢ − x̄)²; SSB = a·r·Σ(x̄ⱼ − x̄)²; SSAB = r·Σ(x̄ᵢⱼ − x̄ᵢ − x̄ⱼ + x̄)²; SSE = Σ(x − x̄ᵢⱼ)². F = MS ÷ MSE with df (a−1), (b−1), (a−1)(b−1) and ab(r−1).
Method: Balanced two-way ANOVA with interaction (Fisher), per ISO 16269-1. The p-values are computed from the F distribution itself (incomplete beta function). The design must be balanced: the same number of replicates in every cell.
Assumptions: the observations are independent, approximately normal within each cell, with equal variance across cells; the design is balanced.
Limitations: an unbalanced design (unequal replicates) needs a different calculation — this tool refuses it rather than guessing. A significant interaction means the main effects cannot be read on their own.
Rounding: F values to 4 decimal places; p to 4 decimal places; sums of squares to 2 decimal places; intermediates unrounded.
This is a calculation aid, not a laboratory report — confirm against your accredited method before citing a value.
Method: Balanced two-way ANOVA with interaction (Fisher), per ISO 16269-1. The p-values are computed from the F distribution itself (incomplete beta function). The design must be balanced: the same number of replicates in every cell.
Assumptions: the observations are independent, approximately normal within each cell, with equal variance across cells; the design is balanced.
Limitations: an unbalanced design (unequal replicates) needs a different calculation — this tool refuses it rather than guessing. A significant interaction means the main effects cannot be read on their own.
Rounding: F values to 4 decimal places; p to 4 decimal places; sums of squares to 2 decimal places; intermediates unrounded.
This is a calculation aid, not a laboratory report — confirm against your accredited method before citing a value.
Worked example: 2 × 2 with 3 replicates: cells (6,8,7), (10,12,11), (4,5,6), (8,9,10): F(A) = 12.0000 (p 0.0085), F(B) = 48.0000 (p 0.0001), F(A×B) = 0.0000 (p 1.0000).
Enter values above to see results.
Enter values cell by cell in the order A1B1, A1B2, …, A2B1, A2B2 — the tool checks the count matches a × b × replicates. Tool 307 of 500 — GIFSQ
